Permutation Arrays Under the Chebyshev Distance

Klve, Torleiv; Lin, Tsung-Chieh; Tsai, Shi-Chun; Tzeng, Wen-Guey

doi:10.1109/tit.2010.2046212

Cited by 123 publications

(79 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, some works focus on codes in S n with Hamming distance [1], [2], and some others investigate the error correction problem under metrics such as Chebyshev distance [3] and Kendall tau distance [4].…”

Section: Introductionmentioning

confidence: 99%

A rate-distortion theory for permutation spaces

Wang¹,

Mazumdar

Wornell³

2013

2013 IEEE International Symposium on Information Theory

View full text Add to dashboard Cite

Abstract-We investigate the lossy compression of the permutation space by analyzing the trade-off between the size of a source code and the distortion with respect to either Kendall tau distance or 1 distance of the inversion vectors. For both distortion measures, we characterize the rate-distortion functions and provide explicit code designs that achieve them. Finally, we provide bounds on the higher order terms in the codebook size when the distortion levels lead to degenerate code rates (0 or 1).

show abstract

Section: Introductionmentioning

confidence: 99%

A rate-distortion theory for permutation spaces

Wang¹,

Mazumdar

Wornell³

2013

2013 IEEE International Symposium on Information Theory

View full text Add to dashboard Cite

show abstract

“…One of the key ingredients of our constructions is permutation interleaving, which we proposed for Ulam metric code design in [7]. The related idea of restricting certain positions in the codewords to certain values was first described in [11], [12], while interleaving in the Chebyshev metric was discussed in [18].…”

Section: Constructionsmentioning

confidence: 99%

“…The Ulam distance has also received independent interest in the bioinformatics and the computer science communities for the purpose of measuring the "sortedness" of data [9]. Other metrics used for permutation code construction include the Hamming distance [2], [10] and the Chebyshev distance (the ℓ ∞ metric) [11], [12].…”

Section: Introductionmentioning

confidence: 99%

Multipermutation Codes in the Ulam Metric for Nonvolatile Memories

Farnoud

Milenković

2014

IEEE J. Select. Areas Commun.

View full text Add to dashboard Cite

Abstract-We address the problem of multipermutation code design in the Ulam metric for novel storage applications. Multipermutation codes are suitable for flash memory where cell charges may share the same rank. Changes in the charges of cells manifest themselves as errors whose effects on the retrieved signal may be measured via the Ulam distance. As part of our analysis, we study multipermutation codes in the Hamming metric, known as constant composition codes. We then present bounds on the size of multipermutation codes and their capacity, for both the Ulam and the Hamming metrics. Finally, we present constructions and accompanying decoders for multipermutation codes in the Ulam metric.

show abstract

“…For example, for flash memory coding, Kløve et al gave a new construction for permutation codes based on Chebyshev Distance [11], which is an appropriate distance measure for flash memory coding. Barg and Mazumdar [24] also studied some fundamental bounds on permutation codes in terms of the Kendall tau distance.…”

Section: Arxiv:10116441v3 [Csit] 8 Jul 2011mentioning

confidence: 99%

LP-Decodable Permutation Codes Based on Linearly Constrained Permutation Matrices

Wadayama

Hagiwara

2012

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding problem for the proposed class of permutation codes as a linear programming (LP) problem. The main feature of this class of permutation codes, called LP decodable permutation codes, is this LP decodability. It is demonstrated that the LP decoding performance of the proposed class of permutation codes is characterized by the vertices of the code polytope of the code. Two types of linear constraints are discussed; one is structured constraints and another is random constraints. The structured constraints such as pure involution lead to an efficient encoding algorithm. On the other hand, the random constraints enable us to use probabilistic methods for analyzing several code properties such as the average cardinality and the average weight distribution.

show abstract

Permutation Arrays Under the Chebyshev Distance

Cited by 123 publications

References 10 publications

A rate-distortion theory for permutation spaces

A rate-distortion theory for permutation spaces

Multipermutation Codes in the Ulam Metric for Nonvolatile Memories

LP-Decodable Permutation Codes Based on Linearly Constrained Permutation Matrices

Contact Info

Product

Resources

About